Spin ice, fractionalization, and topological order

The spin ice compounds Dy ₂Ti ₂O ₇ and Ho ₂Ti ₂O ₇ are highly unusual magnets that epitomize a set of concepts of great interest in modern condensed matter physics: Their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles that arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics, and dynamics - in and out of equilibrium - of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable Dirac strings, and irrational charges. We close with the outlook for these unique materials.